asymptotic tight bound for quadratic functions

Question

In CLRS (Introduction to Algorithms by Cormen, Leiserson, Rivest, and Stein), for a function

f(n) = an² + bn

Answer 1

To prove that any polynomial f(n)=a0+a1*n+a2*n^2+a3*n^3+...+am*n^m is theta(n^m), follow two simple steps. step 1. show that f(n) is bigOh(n^m) step 2. show that f(n) is bigOmega(n^m)

If both the above conditions hold good, then definitely f(n) is bigTheta(n^m).

This is a generalization. By putting m=2, you get f(n) is bigTheta(n^2) Simple.. isn't it?